Nuprl Lemma : band-is-inl
∀[a,b:Top + Top]. ∀[c:Top]. (a ~ inl outl(a)) ∧ (b ~ inl outl(b)) supposing (a ∧b b) = (inl c) ∈ (Top + Top)
Proof
Definitions occuring in Statement :
band: p ∧b q,
outl: outl(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
inl: inl x,
union: left + right,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
outl: outl(x),
bfalse: ff,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
true: True,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
bool: 𝔹,
top: Top
Lemmas referenced :
top_wf,
subtype_base_sq,
int_subtype_base,
equal_wf,
bfalse_wf,
subtype_rel_union,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
sqequalHypSubstitution,
applyEquality,
lambdaEquality,
natural_numberEquality,
unionEquality,
lemma_by_obid,
hypothesis,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
promote_hyp,
independent_pairFormation,
because_Cache,
productElimination,
independent_pairEquality,
sqequalAxiom,
hypothesisEquality,
isect_memberEquality,
voidEquality,
inlEquality
Latex:
\mforall{}[a,b:Top + Top]. \mforall{}[c:Top]. (a \msim{} inl outl(a)) \mwedge{} (b \msim{} inl outl(b)) supposing (a \mwedge{}\msubb{} b) = (inl c)
Date html generated:
2016_05_13-PM-04_00_03
Last ObjectModification:
2015_12_26-AM-10_49_37
Theory : bool_1
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